I searched for the word "proselytize" on accesstoinsight and found it in only two articles. One is Ven. Bhikkhu Bodhi saying (talking about religion in general in the modern world, not only about Buddhism),
The two religious phenomena that in my view are false detours which must finally be rejected are fundamentalism and spiritual eclecticism. Both have arisen as reactions to the pervasive secularism of our time; both speak to the widespread hunger for more authentic spiritual values than our commercial, sensualist culture can offer. Yet neither, I would argue, provides a satisfactory solution to our needs.
Fundamentalism no doubt bears the character of a religious revival. However, in my opinion it fails to qualify as a genuinely spiritual type of religiosity because it does not meet the criterion of true spirituality. This criterion I would describe, in broad terms, as the quest to transcend the limitations of the ego-consciousness. As I understand fundamentalism, it draws its strength from its appeal to human weakness, by provoking the ego-consciousness and the narrow, volatile interests of the small self. Its psychological mood is that of dogmatism; it polarizes the human community into the opposed camps of insiders and outsiders; it dictates a policy of aggression that entails either violence against the outsiders or attempts to proselytize them. It does not point us in the direction of selflessness, understanding, acceptance of others based on love, the ingredients of true spirituality.
Spiritual eclecticism — omnipresent in the West today — is governed by the opposite logic. It aims to amalgamate, to draw into a whole a sundry variety of quasi-religious disciplines: yoga, spiritualism, channeling, astrology, faith healing, meditation, I Ching, special diets, Cabbala, etc. These are all offered to the seeker on a pick-and-choose basis; everything is valid, anything goes. This eclecticism often reveals a longing for genuine spiritual experience, for a vision of reality more encompassing than pragmatic materialism. It fails because it tears profound disciplines out from their context in a living faith and blends them together into a shapeless mixture without spine or substance. Its psychological mood is that of a romantic, promiscuous yearning for easy gratification rather than that of serious commitment. Owing to its lack of discrimination it often shades off into the narcissistic and the occult, occasionally into the diabolical.
I think that's saying that a "fundamentalist" (and ego-maniacal) view divides the world into insiders and outsiders (e.g. Buddhists and non-Buddhists), and attempts to proselytize the outsiders, instead of being selflessness, understanding, and accepting of others based on love.
Another is this Personal Observation
When I first came to Sri Lanka from America, I had just about given up all hope of living. The doctors in America had provided me with maybe twenty-five different drugs for a very bad heart condition and other ailments. We fled America, my husband and I, to live out our lives among peaceful surroundings — in the heart of Buddha-land. Shortly after arrival, what with the long trip and thoughts of death, I truly was dying. I had a myocardial infarction and was taken to the hospital. I found the hospital conditions so deplorable, I felt it would be better to die in bed at home. Consequently, I left the hospital. My husband had found a lovely home for us and there I waited to die. After much pain and emotional upheaval my husband found an anagarika, a Buddhist lay brother, who came to our home and performed a miracle, or to state it better, pointed out to me the "path" that I shall follow for the rest of my days here on earth. This monk-like follower of the Buddha, the Anagarika Tibbotuwawa, instructed me in meditation.
We went through four stages and in time I threw out all drugs, and the life "here and now" became clear and meaningful. Many strange things began to occur in the course of meditation. First I began to feel that I was on another plane of consciousness. I no longer had a self, sick or otherwise. I was at one with all, all of us in a new world, with all non-beings too. I found that the "ego" that nearly wrecked my life was now gone. I felt reborn, and extended my meditation to vibrations of loving-kindness. Thought messages I call them. Then one morning a friend called from America. On the phone he said that he had received my message. He was elated beyond belief, thanked me and promised to come here in the near future. The strangest of all was a telegram from my sister. She asked if we could accommodate her at our home in three weeks. I nearly had a heart attack! My sister is seventy-eight years old. I had heard no word from her for fifteen years. Yet I had been sending her "thought messages" of loving-kindness, and her image was growing clearer and clearer — even before arrival. She was "with me" even before arrival. At age seventy-eight she had traveled half-way around the world to see me. When she arrived she said she had had a compelling urge to see me. We were both delighted and, to my amazement, she meditated each evening with me and said she had never known such "peace and love" as she found in our home.
She could not remain with us, as I had hoped, but had responsibilities at home that she felt better able to cope with now. She left, adding, "I have promises to keep — and many miles to go before I sleep."
These few experiences have been so uplifting that now, even though I never proselytize, many young people come to me for instruction in meditation. Recently a young man from Switzerland came to our home. He felt he was dying of rabies ("rabbits" he called it in broken English). I was so sure he did not have this disease that I suggested that he meditate with me and Anagarika that day, and he seemed pleased with the experience. Well, this young man came not only each evening, but also every morning at 5:30 a.m. bringing fresh flowers for the Buddha. He left, after three weeks of intensive meditation and instruction and reading of the Dhamma, well and happy and full of ideas to help suffering humanity.
There are, of course, many ideas I have omitted which are advanced procedures in insight meditation, the three stages which usually follow the concentration on breathing. These are body, feelings, perceptions and consciousness, ultimately expressing themselves in "the mind experiencing pure mind." I feel, however, that the reader can find these steps in many publications that have been released on this subject. If this booklet helps the beginner with just a little insight into the "way" and the "why" of meditation, this will be my happiness.
Apart from the fact that she "never proselytizes" there's the story of the "Buddhist lay brother" in the first paragraph: i.e. a person who needed him went looking for him.
Perhaps the best way to spread Buddhism is to cultivate it within yourself (?and make yourself available).
I've also seen "Dharma books" being spread: e.g. I have a book published by these people in Taiwan, which I found free of cost from a temple in Canada. Or in the same way that Gideon Bibles are famously found for free in hotel rooms, in some countries (Singapore) you find a Buddhist 'bible' in the hotel room.
Finally, I presume that what is said about Right Speech is applicable to talking about Dharma.